The Oberndorf style was all I could find when I was shopping for 416 Rem bottom metal when building my 404J (Sunny Hill would make 404J bottom metal for me but $700 pricetag was too much). I don't think it's that big an issue if the release is stiff enough. Some makers sell them with adjustable release. Mine from Swift-Blackburn required some fine tuning. Any hunter holding a 375 so loosely that his finger hits the release during firing will probably have other issues to worry about. Like scope or thumb hitting him in the face. I don't see accidentally releasing the floorplate being much concern if you spend some time learning to shoot your gun.
Again, note that the magazine box is deeper on NECG Model 640. It will hang below your current stock. If the floorplate is wider than the magazine, and most are to conceal the contact area around the magazine box, then that would be a problem for you. Besides being unsightly, the exposed floorplate overhang could get caught on stuff. It is hard to tell from the photo if the edge of floorplate is flush to the sides of magazine but I seriously doubt it. If not, then a custom stock with deeper mag well would be required.